Math Problem Statement
Solution
To solve this problem, we need to determine the number of prime numbers in each specified interval. Here's how we can find these values:
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Interval 0 to 40: We count the primes between 0 and 40:
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There are 12 primes in this range. -
Interval 40 to 80: Primes between 40 and 80 are:
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There are 10 primes in this range. -
Interval 80 to 120: Primes between 80 and 120 are:
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There are 8 primes in this range. -
Interval 120 to 160: This interval was provided with the correct answer of 7 primes.
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Interval 160 to 200: Primes between 160 and 200 are:
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There are 9 primes in this range.
Summary of Answers
- 0 to 40: 12
- 40 to 80: 10
- 80 to 120: 8
- 120 to 160: 7 (already correct)
- 160 to 200: 9
Let me know if you'd like further details on any of the calculations, or if you have other questions.
Related Questions
- How are prime numbers distributed in other intervals, like 200 to 300?
- What methods can help efficiently find the number of primes in large intervals?
- How do we prove there are infinitely many prime numbers?
- What are some patterns observed in prime numbers across different ranges?
- Can prime number density be approximated in any range using a formula?
Tip
A useful tool for finding prime numbers in a range is the Sieve of Eratosthenes algorithm, which efficiently finds all primes up to a given limit.
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Math Problem Analysis
Mathematical Concepts
Prime Numbers
Number Theory
Intervals
Formulas
Prime counting within intervals
Theorems
Infinitude of Primes
Prime Number Theorem
Suitable Grade Level
Grades 9-12
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